Problem $2.(45$ points$)$ PROCESS ANALYSIS.

HealthyCare Hospital specializes in providing outpatient orthopedic surgeries to patients in a

busy urban area. Lately, the hospital has been receiving complaints about extended wait times

and is seeking your assistance in investigating the issue. The process involves several steps,

starting with patient check$-$in$,$ medical history and insurance form completion, preparation in an

examination room, surgery in an operating room, and post$-$surgery recovery. Each of these steps

requires various resources and time, as shown in the table below:

Resources Task Average Time $($minutes$)$

Receptionist Check$-$in $6$

Nurse, Exam Room Preparation $15$

Anesthesiologist, Op$.$ Room Anesthesia $20$

Anesthesiologist, Surgeon, Nurse, Op$.$ Room Surgery $50$

Receptionist Check$-$out $3$

The hospital has $1$ receptionist, $4$ nurses, $2$ exam rooms, $2$ anesthesiologists, $2$ surgeons, $2$ operating

rooms, and $2$ recovery rooms.

a$)(3$ points$)$ What is the raw process time $($flow time in system with no waiting$)$ of a patient in

this process $($in minutes$)?$ Assume all resources are available whenever needed and there are

no delays between tasks $($e$.$g$.,$ you may ignore the time the patient spends walking or getting

transported between tasks$).$

b$)(12$ points$)$ Complete the table below. Determine the total workload assigned to each

resource per patient. Show all your work and fill in the answers in the table. Notice that you

will compute the capacity of each resource. Note that $$pat$/$hr$$ refers to $$patients per hour$.$

Resource

Processing

Time

$($min$/$pat$)$

Capacity of

each Resource

$($pat$/$hr$/$resource$)$

Number of Resources

per Resource Type

Capacity of

Resource Type

$($pat$/$hr$)$

Receptionist

Nurse

Exam Room

Anesthesiologist

Op$.$ Room

Surgeon

The hospital has $1$ receptionist, $4$ nurses, $2$ exam rooms, $2$ anesthesiologists, $2$ surgeons, $2$ operating

rooms, and $2$ recovery rooms.

a$)(3$ points$)$ What is the raw process time $($flow time in system with no waiting$)$ of a patient in

this process $($in minutes$)?$ Assume all resources are available whenever needed and there are

no delays between tasks $($e$.$g$.,$ you may ignore the time the patient spends walking or getting

transported between tasks$).$

b$)(12$ points$)$ Complete the table below. Determine the total workload assigned to each

resource per patient. Show all your work and fill in the answers in the table. Notice that you

will compute the capacity of each resource. Note that "pat$/$hr$"$ refers to "patients per hour".

c$)(3$ points$)$ What is the hourly capacity $($i$.$e$.,$ maximum hourly throughput rate$)$ of the process?

Your answer should be in number of patients per hour $($pat$/$hr$).$

d$)(3$ points$)$ Which resource $($or resources$)$ is $($are$)$ the bottleneck of this process?

e$)(4$ points$)$ What is the hourly utilization rate of nurse if the bottleneck$($s$)$ work nonstop $($i$.$e$.,$

works at capacity$)?$ Keep in mind that the non$-$bottleneck resources may be idle during the

day because the process follows the pace of the bottleneck resource and that a patient is

served completely on the day they arrive, i$.$e$.,$ there is no work$-$in$-$process remaining at the

end of the day.

f$)(20$ points$)$ Hospital decides to update the process in the following way: add another

operating room which costs $$1000/$hr and the anesthesiologist stays only for $30$ minutes of

each surgery instead of the current $45$ minutes on the average. You can ignore the fixed cost

of constructing a new operating room.

i$.(6$ points$)$ Update the capacity of the operating rooms and the anesthesiologists.

ii$.(2$ points$)$ Which resource $($or resources$)$ is $($are$)$ the bottleneck of this process after the

change?

iii. $(2$ points$)$ What is the capacity of the process now?

iv$.(6$ points$)$ Compute the incremental benefit of this change in $$/$day$?$ Assume that the

process can work at its capacity. Hint: Consider the increase in the capacity thanks to

this change.

v$.(4$ points$)$ Is updating process feasible? Prove your answer by comparing the

incremental benefit with the incremental cost of the change.